If Party A and Party B purchase tickets separately, the two groups will have to pay 1 142 yuan; If they buy air tickets together as a group, they should pay a total of 864 yuan.

After joining the group, the amount is 864 yuan and the number of people is an integer.

864 \ 12 = 72 & gt； 50, unqualified

864÷ 10=86.4 is not an integer, which is unqualified.

864÷8 = 108 & gt； 100 people, eligible.

If there are more than 50 people in both groups, the total amount is108 *10 =1080 ≠1142.

(The following chickens and rabbits are in the same cage)

Price difference between 50 people and 50- 100 = 2 yuan.

(1142-1080) ÷ (12-10) = 31person,

108-3 1=77 people

The number of small groups is 3 1, and the number of large groups is 77.